I am new to DSLRs and RAW images so please bare with me if this is extremely amateur. I keep trying to take RAW pictures but every single one of them shows up with an extremely blue "overlay" type layer. Is there something I'm doing wrong?

I am using a Sony Alpha a33 and I have used Picasa, Gimp, and Shotwell (linux).

The output you'll get from a RAW file is highly dependent on the tools you're using. For instance, when I open your RAW file in Preview on OS X this is the result:

No blue overlay. I would guess that the RAW profile (meaning the default output from a RAW file produced from a given camera) used by the tools you're using for your camera is not very good. Maybe try updating them, or if that doesn't work simply apply some temperature adjustments to all the images you process. You could always stick with JPEG if you're not going to be taking advantage of the increased adjustments you can perform with RAW images.

It seems to be a white balance issue, which may be compounded by a slight under-exposure.

I opened the file with UFRaw (Gimp's Raw Conversion tool) and used the sliders to adjust the white balance and the green level.

It's a bit tricky as I don't really know what the room should look like, but I think It's probably close.

A good way to handle this is to set a custom white balance:

Custom white balance is set by
selecting Custom Setup from the white
balance menu, and pointing the camera
at a neutral white or grey card under
the lighting you'll be shooting in,
filling a frame in the center of the
display with the reference target,
then pressing the Shutter button.